For the experiments on the datasets DSprites [1]}, Shapes3D [2]}, Cars3D [3]}, SmallNORB [4]}, we implement a simple convolutional architecture for both the encoder and the decoder. We report the detailed parameters in Table REF , where \(d\)  refers to the dimensionality of the latent space \(\mathcal {Z}\) , which bounds the maximum dimensionality of each of the \(k\)  latent subspaces \(\mathcal {S}_1 \ldots \mathcal {S}_k\) . The architecture of the nonlinear projectors \(P_i\)  is described in Table REF .
For the FAUST dataset we employ a PointNet [5]} based architecture for the encoder and a simple MLP for the decoder. Details are reported in Table  REF
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